The Prime Minister did not meet Mr Hollande when he visited Paris in February and had indicated his support for Mr Sarkozy in the contest but the pair have agreed to build on the already "very close relationship" between the two nations.

A Number 10 spokeswoman said: "The Prime Minister called President-Elect Hollande this evening and congratulated him on his victory.

"They both look forward to working very closely together in the future and building on the very close relationship that already exists between the UK and France."

In his victory speech Mr Hollande said he was "proud to have been capable of giving people hope again".

Labour leader Ed Miliband said: "I congratulate Francois Hollande on his election as President of France.

"I know from our conversations in London earlier this year and from his victory speech of his determination to help create a Europe of growth and jobs, in a way that is responsible and sustainable.

"This new leadership is sorely needed as Europe seeks to escape from austerity. And it matters to Britain.

"In his own campaign, he has shown that the centre-left can offer hope and win elections with a vision of a better, more equal and just world.

"I look forward to working together with him in the months and years ahead."

In a letter, Welsh First Minister Carwyn Jones congratulated Mr Hollande on his "superb and historic" election.

He added: "Your victory has given all socialist sister parties across Europe, great hope for the future - hope that there is an alternative and principled way forward during these difficult financial and economic times.

"I am proud that France and Wales have many things in common - not least our shared passion for rugby. I look forward to welcoming you to Cardiff, when France next play Wales."

Following his election success, Mr Hollande was hailed as a force for further European integration - despite fears that his differences over economic policy will deepen rifts in Brussels.

The new French president is determined to re-open the EU's new "fiscal treaty" to balance its austerity drive with together commitments on restoring growth.

The move, signalled early on in his presidential election campaign, puts him at odds with German chancellor Angela Merkel and her insistence on austerity measures as a priority to prop up the eurozone.

But Mr Hollande's arrival in the family on EU leaders is also likely to put him at odds with Prime Minister David Cameron over a tax on financial services - which the UK refuses to consider - and the prospect of a new French assault on the multi-billion pounds a year rebate on Britain's EU budget payments.

EU officials in Brussels believe Mr Hollande will swiftly deploy renewed French clout in the Union to shake up the current carefully-laid economic strategy of tough budget discipline on eurozone economies and enforced austerity on counties needing bail-outs.

Already, before the election result, the EU's Economic Affairs Commissioner had signalled a new emphasis on growth, after months in which EU policy had been driven by the Franco-German austerity-driven strategy.

But the so-called Merkozy double act of Merkel and Sarkozy is now over and relations are likely to be strained between Berlin and Paris until it becomes clear how far Mr Hollande will go in pushing his French ideas on what the EU's growth pact should look like.

Meanwhile, European Commission President Jose Manuel Barroso issued a formal statement congratulating the new occupant of the Elysee Palace, declaring: "I know I can count on the personal engagement of Francois Hollande to advance European integration."

Mr Barroso insisted that he shared Mr Hollande's conviction that investment in growth was the way forward and that the EU aim now would be to generate durable economic growth and jobs.

But Ukip leader Nigel Farage predicted the new Hollande economic approach would split the Franco-German alliance:

"Hollande's election is great news," he said. "It will help drive a wedge between Germany and France, the two of the engines of EU integration.

"The friction between German austerity and French profligacy will increase and bring the eventual demise of the EU even closer."

The Party of European Socialists said the arrival of the new French president was "a victory for progress in France and in Europe".

PES President Sergei Stanishev said: "The election of a socialist to the Elysee is a great day, not only for France, but for Europe. It is a profound rejection of the Merkozy madness that has choked European economic growth for the last two years."

Martin Schulz, the German president of the European Parliament, commented: "Congratulations to Francois Hollande. Now it's time for a change of direction in Europe.

"On top of fiscal consolidation, which is necessary, the EU is now ready for a growth policy, which is what the European Parliament has been calling for a long time".

Liberal leader in the European Parliament Guy Verhofstadt said former President Sarkozy's stand on the eurozone crisis had been "disappointing and alarming", but Francois Hollande was now promising to "bring his country back into a European dynamic".

Mr Verhofstadt went on: "With him, new prospects will open up for the economic governance of the eurozone."